Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Exact solutions of variable-arc-length elasticas under moment gradient

  • Published : 1997.09.25
⟨ Previous Next ⟩

Abstract

This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fixed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.

Keywords

References

  1. Barten, H.J. (1994), "On the deflection of a cantilever beam", Q. Appl. Math., 2: 168-171.
  2. Bisshopp, K.E. and Drucker, D.C. (1945), "Large deflection of cantilever beams", Q. Appl. Math., 3: 272-275. https://doi.org/10.1090/qam/13360
  3. Bottega, W.J. (1991), "Peeling and bond-point propagation in a self-adhered elastica", Q. Jl. Mech. & Appl. Math., 44., 601-617. https://doi.org/10.1093/qjmam/44.4.601
  4. Britvec, S.J. (1993), The Stability of Elastic Systems, Pergamon Press, New York, 137-195.
  5. Byrd, P.F. and Friedman, M.D. (1971), Handbook of Elliptic Integrals for Engineers and Scientists, Springer, Berlin.
  6. Chucheepsakul, S., Buncharoen, S. and Huang, T. (1995), "Elastica of simple variable-arc length beam subjected to end moment", J. Engrg. Mech., ASCE, 121(7), 767-772. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:7(767)
  7. Chucheepsakul, S., Buncharoen, S., and Wang, C.M. (1994), "Large deflection of beams under moment gradient", J. Engrg. Mech., ASCE, 120(9), 1848-1860. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:9(1848)
  8. Chucheepsakul, S., Theppitak, G., and Wang, C.M. (1996), "Large deflection of simple variable-arc-length beam subjected to a point load", Struct. Engrg. & Mech., An Int'l Journal, 4(1), 49-59. https://doi.org/10.12989/sem.1996.4.1.049
  9. Conway, H.D. (1947), "The large deflection of a simple supported beam", Phil. Mag. Series, 7, 38, 905-911.
  10. Conway, H.D. (1956), "The nonlinear bending of thin circular rods", J. Appl. Mech., 23, 7-10.
  11. Frisch-Fay, R. (1962), Flexible Bars, Butterworths, London, England.
  12. Kempf, J. (1987), Numerical Software Tools in C, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. NJ., 178-180.
  13. Lau, J.H. (1982), "Large deflections of beams with combined loads", J. Engrg. Mech., ASCE, 108(1), 180-185.
  14. Love, A.E.H. (1944), A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 401-405.
  15. Navaee, S. and Elling, R.E. (1992), "Equilibrium configurations of cantilever beams subjected to inclined end loads", J. Appl. Mech., 59(3), 572-579. https://doi.org/10.1115/1.2893762
  16. Navaee, S. and Elling, R.E. (1993), "Possible ranges of end slope for cantilever beams", J. Engrg Mech., ASCE, 119(3), 630-635. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:3(630)
  17. Schile, R.D. and Sierakowski, R.L. (1967), "Large deflection of a beam loaded and supported at two points", Int. J. Non-linear Mech., 2, 61-68. https://doi.org/10.1016/0020-7462(67)90019-4
  18. Seide, P. (1984), "Large deflections of a simply supported beam subjected to moment at one end", J. Appl. Mech., 51(3), 519-525. https://doi.org/10.1115/1.3167667
  19. Thepphitak, G. (1995), "Large deflection analysis of variable-arc-length beams under various loading conditions", KMITT, Bangkok, Thailand.
  20. Wang, C.M. and Kitipornchai, S. (1992), "Shooting-optimization technique for large deflection analysis of structural members", Engrg. Struct., 14(4), 231-240. https://doi.org/10.1016/0141-0296(92)90011-E
  21. Wang, C.M., Lam, K.Y., He, X.Q., and Chucheepsakul, S. (1997), "Large deflections of an end supported beam subjected to a point load", Int. J. Non-linear Mech., 32, 63-72. https://doi.org/10.1016/S0020-7462(96)00017-0

Cited by

  1. DIVERGENCE INSTABILITY OF VARIABLE-ARC-LENGTH ELASTICA PIPES TRANSPORTING FLUID vol.14, pp.6, 2000, https://doi.org/10.1006/jfls.2000.0301
  2. Double Curvature Bending of Variable-Arc-Length Elasticas vol.66, pp.1, 1999, https://doi.org/10.1115/1.2789173
  3. Large deflections of spatial variable-arc-length elastica under terminal forces vol.32, pp.4, 2009, https://doi.org/10.12989/sem.2009.32.4.501
  4. Elastica of a variable-arc-length circular curved beam subjected to an end follower force vol.49, 2013, https://doi.org/10.1016/j.ijnonlinmec.2012.10.002
  5. A New Quasi-Linearization Finite Difference Scheme for Large Deflection Analysis of Prismatic and Non-Prismatic Inextensible Slender Beams vol.9, pp.2, 2006, https://doi.org/10.1260/136943306776986949
  6. Effect of Material Nonlinearity on Large Deflection of Variable-Arc-Length Beams Subjected to Uniform Self-Weight vol.2012, 2012, https://doi.org/10.1155/2012/345461
  7. Effect of inclination on bending of variable-arc-length beams subjected to uniform self-weight vol.30, pp.4, 2008, https://doi.org/10.1016/j.engstruct.2007.04.010